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Math Help - Inverse of function WITH a limit??

  1. #1
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    Inverse of function WITH a limit??

    Find f^-1(x) <-- inverse if f(x) = x^2 - 4x + 3, x <= 2 find value of f^-1(8).


    I got x=29 BUT x<= 2????
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  2. #2
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    Quote Originally Posted by mwok View Post
    Find f^-1(x) <-- inverse if f(x) = x^2 - 4x + 3, x <= 2 find value of f^-1(8).


    I got x=29 BUT x<= 2????
    What did you find your inverse function to be?

    Is it f^{-1}(x)=\pm\sqrt{x+1}+2?
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    Quote Originally Posted by masters View Post
    What did you find your inverse function to be?

    Is it f^{-1}(x)=\pm\sqrt{x+1}+2?
    I just replaced x with y so my inverse function became

    inverse(x) = y^2 - 4y + 3

    which yield 29....is that correct? can't be cause x should be less than 2 (or equal to)
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    Quote Originally Posted by mwok View Post
    I just replaced x with y so my inverse function became

    inverse(x) = y^2 - 4y + 3

    which yield 29....is that correct? can't be cause x should be less than 2 (or equal to)
    Not quite. Your original function was f(x)=x^2-4x+3

    f(x)=y=x^2-4x+3

    Interchange x and y

    x=y^2-4y+3

    Isolate the y

    y^2-4y=x-3

    Complete the square on the left side. You'll see why in a minute.

    y^2-4y+4=x-3+4

    (y-2)^2=x+1

    y-2=\pm\sqrt{x+1}

    y=\pm\sqrt{x+1}+2

    \boxed{f^{-1}(x)=\pm\sqrt{x+1}+2}
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    Wow! I didn't know you could plus 4 to each side and solve the problem like that. Are there multiple ways to solve this?
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    Quote Originally Posted by mwok View Post
    Wow! I didn't know you could plus 4 to each side and solve the problem like that. Are there multiple ways to solve this?
    You could've used the quadratic formula, but completing the square seems to be the best way.

    Now, can you find f^{-1}(8) ?
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    Quote Originally Posted by masters View Post
    You could've used the quadratic formula, but completing the square seems to be the best way.

    Now, can you find f^{-1}(8) ?
    Yep, got it. It can either be -1 or 5 BUT since x should be less or equal to 2, it is automatically -1.

    Thanks so much!
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